Scientific reasoning based on the biology of HIV justifies the use of Poisson statistics as the approximate probability distribution underlying infection by HIV in chimpanzee trials. A statistic S using Bayesian predictive probabilities was used to generate P-values for assessing the statistical significance of various HIV trials in chimpanzees in frequentist Monte Carlo simulations. Computer simulations showed that even sparse infectivity data from chimpanzee trials can be statistically significant and that this significance was remarkably robust against large perturbations away from the ideal Poisson probability distribution. The computer simulations showed that in hypothetical repetitions of some (but certainly not all) actual trials, the values S produced in simulation were smaller than the corresponding actual trial value S[0] in fewer than 0.05 of the computer runs, indicating statistical significance under the usual frequentist criterion. Given certain biological assumptions, these methods provide an objective basis for assessing HIV trials in chimpanzees.